This page is maintained to log whatever silly ideas I get while working various problems I face time and again. Probably every academic stream under the sky is dealt at some point of time; some I forget instantly, others I remember for a long time. Here are some opinions that I came up with and, mistakenly remembered. In other words, it's just the useless and pointless knowledge of mine that you'll encounter here. So you better move away!
Disclaimer
I hereby declare that the opinions expressed on this page are personal and the Institute or any of its authorities, faculty members, students and rest of the employees have nothing to do with them any way imaginable. You may find some views offinsive, some profane and some outrightly disgusting. You can't help it! Niether can anyone else, unless there is a rule that I must abide in order to not post them on this server. Sadly, there is no such rule, so if you have not left this page by now, or do not want to leave, you're responsible for any offense you take. I would advise keeping those feelings aside.
- Does P = NP? (See the image above.)
Almost all serious computer scientists in the world shall answer “nope, nada, no way!” to that question. I'm not a serious scientist from any stretch of imagination! Still... My answer is the same. In all probability, P does not equate to NP. Surprised, huh?
Before dealing with the real question, let us deal with a trivial one. Why do I think the problem is even worth consideration of a thought? I think the problem is very deep! Deeper than any other deep problem in mathematics. No, the problems that have already been proved to be unsolvable are not this deep, simple because there is already a concrete statement said about them!
If you had an “efficient” method to solve the problems in the complexity class NP-complete, you could solve P = NP?, and you would also solve almost all problems in mathematics, simply writing a program to search through all possible proofs in some formal system. So if P equates NP, we have very profound implications in the world of mathematics. It would turn out that all the efforts put in so far, well, at least after the question was posed, to prove astonishing results were futile!
The ‘depth’ of the question and its profound philosophical or practical implications don't mean the solution to it has to be tough, it may or may not be, and we'll not argue about the fact that it is exteremely hard, or it is beyond the scope of current mathematical techniques. Rest all about it is philosophical and symbolic gibberish, so I won't go into that here, however much I like that gibberish and want to go into that.